EDIT: I'll leave my original work in here, but it's wrong!!!!
The real answer can be found here:
http://www.pokerforums.org/showthrea...362#post130362
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Total Flop Combinations = 50 x 49 x 48 =
117600
Flush Draw:
You need two hearts on the flop. There are 11 cards for 1 heart and 10 more for the second (9 more to complete the flush). 39 non-hearts.
Combinations:
11 x 10 x 9 = 990 (completes flush)
11 x 10 x 39 = 4290
11 x 39 x 10 = 4290
39 x 11 x 10 = 4290
Total =
13860 flops / 117600 =
11.79%
Trips/Quads/Full House:
You need one of 3 cards to pair. One of 2 cards to hit trips. Then any of 47 cards (3 give you FH). And then its x2 to account for both hole cards.
Combinations:
3 x 2 x 1 = 6 (quads)
3 x 2 x 47 = 282
3 x 47 x 2 = 282
47 x 3 x 2 = 282
Total = 852; x 2 to account for both hole cards = 1704
Total =
1704 flops / 117600 =
1.45%
2 Pair:
You need one of 6 cards to pair. Then one of 3 cards for 2 pair. Then one of 42 cards to avoid duplicating trips.
Combinations:
6 x 3 x 42 = 756
6 x 42 x 3 = 756
42 x 6 x 3 = 756
Total =
2268 flops / 117600 =
1.93%
Open Ended Straight Draw (OESD):
There are 3 OESDs that you can flop. Call them nut, middle and idiot. We can figure out combinations of 1 and then x3. We need one of 8 cards for the beginning of OESD and then one of 4 cards to complete OESD. Any of remaining cards after that. Then we have to adjust for duplicating made str8s. Then we have to adjust for duplicating FDs.
8 x 4 x 48 = 1536
8 x 45 x 4 = 1440
42 x 8 x 4 = 1344
Total = 4320; x3 difft OESDs = 12960
I believe there are 24 duplicates in this number, each representing a made str8 (ex. we have 89s: flop of 67T is duplicated because 67x and x7T are different OESDs but can have identical flops). Anyway, I could be wrong, but I'm counting 24 duplicates.
Total =
12936 flops / 117600 =
11.00%
But we have double-counted "Open Ended Str8 Flush Draws". Not totally sure, but I count 432 duplicates.
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So we add up our total "successful" flops:
Flush Draw (non OESFD): 13428 = 11.42%
Str8 Draw (non OESFD): 12504 = 10.63%
Open End Str8 Flush Draw: 432 = 0.37%
2 Pair: 2268 = 1.93%
Trips / Quads / Full House: 1704 = 1.45%
TOTAL = 30336 flops = 25.8%
I got skills, huh? Curious if anybody can verify any of this through another source.
EDIT: There are 384 double gutshot str8 draws that I left out. (19 of which are FDs). And I think I miscounted the OESFDs. I'll update later.
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Correct information can be found here:
http://www.pokerforums.org/showthrea...362#post130362